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a) \(\left(2x^3y-0,5x^2\right)^3\)
\(=\left(2x^3y\right)^3-3\left(2x^3y\right)^20,5x^2+3.2x^3y\left(0,5x^2\right)^2-\left(0,5x^2\right)^3\)
\(=8x^9y^3-6x^8y^2+1,5x^7y-0,125x^6\)
b) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)
\(=x^3-\left(3y\right)^3\)
\(=x^3-27y^3\)
c) \(\left(x^2-3\right)\left(x^4+3x^2+9\right)\)
\(=x^3-3^3\)
\(=x^3-27.\)
a,\(\left(2x^3y-0,5x^2\right)^3=\left(2x^3y\right)^3-3.\left(2x^3y\right)^2.\left(0,5x^2\right)+3.\left(0,5x^2\right)^2.\left(2x^3y\right)-\left(0,5x^2\right)^3\)
\(=8x^9y^3-6x^8y^2+\frac{3}{2}x^7y-\frac{1}{8}x^6\)
b,\(\left(x-3y\right)\left(x^2+3xy+9y^2\right)=\left(x-3y\right)\left[x^2+x.3y+\left(3y\right)^2\right]\)
\(=x^3-\left(3y\right)^3=x^3-27y^3\)
\(\left(x^2-3\right)\left(x^4+3x^2+9\right)=\left(x^2-3\right)\left[\left(x^2\right)^2+3.x^2+3^2\right]\)
\(=\left(x^2\right)^3-3^3=x^6-27\)
a) \(\left(x+3y\right)\left(2x^2y-6xy^2\right)\)
\(=x\left(2x^2y-6xy^2\right)+3y\left(2x^2y-6xy^2\right)\)
\(=2x^3y-6x^2y^2+6x^2y^2-18xy^3\)
\(=2x^3y-18xy^3\)
b) \(\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2\)
\(=6x^5y^2:3x^3y^2-9x^4y^3:3x^3y^2+15x^3y^4:3x^3y^2\)
\(=2x^2-3xy+5y^2\)
c) \(\left(2x+3\right)^2+\left(2x+5\right)^2-2\left(2x+3\right)\left(2x+5\right)\)
\(=\left(2x+3-2x-5\right)^2\)
\(=\left(-2\right)^2=4\)
d) \(\left(y+3\right)^3-\left(3-y\right)^2-54y\)
\(=y^3+9y^2+27y+27-\left(x^2-6x+9\right)-54y\)
\(=y^3+9y^2-27y+27-x^2+6y-9\)
\(=y^3+9y^2-x^2-21y+18\)
a) Ta có: \(\left(x-3\right)^3\)
\(=x^3-3\cdot x^2\cdot3+3\cdot x\cdot3^2-3^3\)
\(=x^3-9x^2+27x^2-27\)
b) Ta có: \(\left(2x-3\right)^3\)
\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2-3^3\)
\(=8x^3-36x^2+54x-27\)
c) Ta có: \(\left(x-\frac{1}{2}\right)^3\)
\(=x^3-3\cdot x^2\cdot\frac{1}{2}+3\cdot x\cdot\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^3\)
\(=x^3-\frac{3}{2}x^2+\frac{3}{4}x-\frac{1}{8}\)
d) Ta có: \(\left(x^2-2\right)^3\)
\(=\left(x^2\right)^3-3\cdot\left(x^2\right)^2\cdot2+3\cdot x^2\cdot2^2-2^3\)
\(=x^6-6x^4+12x^2-8\)
e) Ta có: \(\left(2x-3y\right)^3\)
\(=\left(2x\right)^3-2\cdot\left(2x\right)^2\cdot3y+2\cdot2x\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^3-24x^2y+36xy^2-27y^3\)
f) Ta có: \(\left(\frac{1}{2}x-y^2\right)^3\)
\(=\left(\frac{1}{2}x\right)^3-3\cdot\left(\frac{1}{2}x\right)^2\cdot y^2+3\cdot\frac{1}{2}x\cdot\left(y^2\right)^2-\left(y^2\right)^3\)
\(=\frac{1}{8}x^3-\frac{3}{4}x^2y^2+\frac{3}{2}xy^4-y^6\)
a: \(=4x^2-25-4x^2+12x-9-12x=-34\)
b: \(=8y^3-12y^2+6y-1-2y\left(4y^2-12y+9\right)-12y^2+12y\)
\(=8y^3-24y^2+18y-1-8y^3+24y^2-18y=-1\)
c: \(=x^3+27-x^3-20=7\)
d: \(=3y\left(9y^2+12y+4\right)-27y^3+1-36y^2-12y-1\)
\(=27y^3+36y^2+12y-27y^3-36y^2-12y\)
=0
a) \(\left(2x^2-1\right)^2=\left(2x^2\right)^2-2.2x^2.1+1^2\)
\(=4x^4-4x^2+1\).
b) \(\left(\frac{1}{2}x+3y^2\right)^2=\left(\frac{1}{2}x\right)^2+2.\frac{1}{2}x.3y^2+\left(3y^2\right)^2\)
\(=\frac{1}{4}x^2+3y^2x+9y^4\)
Chúc bn hc tốt!
a) (4x2 – 9y2) : (2x – 3y) = [(2x)2 – (3y)2] : (2x – 3y) = 2x + 3y;
b) (27x3 – 1) : (3x – 1) = [(3x)3 – 1] : (3x – 1) = (3x)2 + 3x + 1 = 9x2 + 3x + 1
c) (8x3 + 1) : (4x2 – 2x + 1) = [(2x)3 + 1] : (4x2 – 2x + 1)
= (2x + 1)[(2x)2 – 2x + 1] : (4x2 – 2x + 1)
= (2x + 1)(4x2 – 2x + 1) : (4x2 – 2x + 1) = 2x + 1
d) (x2 – 3x + xy -3y) : (x + y)
= [(x2 + xy) – (3x + 3y)] : (x + y)
= [x(x + y) – 3(x + y)] : (x + y)
= (x + y)(x – 3) : (x + y)
= x – 3.
Tính nhanh:
a) (4x2 – 9y2) : (2x – 3y); b) (27x3 – 1) : (3x – 1);
c) (8x3 + 1) : (4x2 – 2x + 1); d) (x2 – 3x + xy -3y) : (x + y)
Bài giải:
a) (4x2 – 9y2) : (2x – 3y) = [(2x)2 – (3y)2] : (2x – 3y) = 2x + 3y;
b) (27x3 – 1) : (3x – 1) = [(3x)3 – 1] : (3x – 1) = (3x)2 + 3x + 1 = 9x2 + 3x + 1
c) (8x3 + 1) : (4x2 – 2x + 1) = [(2x)3 + 1] : (4x2 – 2x + 1)
= (2x + 1)[(2x)2 – 2x + 1] : (4x2 – 2x + 1)
= (2x + 1)(4x2 – 2x + 1) : (4x2 – 2x + 1) = 2x + 1
d) (x2 – 3x + xy -3y) : (x + y)
= [(x2 + xy) – (3x + 3y)] : (x + y)
= [x(x + y) – 3(x + y)] : (x + y)
= (x + y)(x – 3) : (x + y)
= x – 3.
a) Ta có: \(\left(x+1\right)^3\)
\(=x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3\)
\(=x^3+3x^2+3x+1\)
b) Ta có: \(\left(2x+3\right)^3\)
\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2+3^3\)
\(=8x^3+3\cdot4x^2\cdot3+27\cdot2x+27\)
\(=8x^3+36x^2+54x+27\)
c) Ta có: \(\left(x+\frac{1}{2}\right)^3\)
\(=x^3+2\cdot x^2\cdot\frac{1}{2}+2\cdot x\cdot\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3\)
\(=x^3+x^2+\frac{1}{2}x+\frac{1}{8}\)
d) Ta có: \(\left(x^2+2\right)^3\)
\(=\left(x^2\right)^3+3\cdot\left(x^2\right)^2\cdot2+3\cdot x^2\cdot2^2+2^3\)
\(=x^6+6x^4+12x^2+8\)
e) Ta có: \(\left(2x+3y\right)^3\)
\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot3y+3\cdot2x\cdot\left(3y\right)^2+\left(3y\right)^3\)
\(=8x^3+36x^2y+54xy^2+27y^3\)
f) Ta có: \(\left(\frac{1}{2}x+y^2\right)^3\)
\(=\left(\frac{1}{2}x\right)^3+3\cdot\left(\frac{1}{2}x\right)^2\cdot y^2+3\cdot\frac{1}{2}x\cdot\left(y^2\right)^2+\left(y^2\right)^3\)
\(=\frac{1}{8}x^3+\frac{3}{4}x^2y^2+\frac{3}{2}xy^4+y^6\)
\(a,\left(3x+5\right)^2=9x^2+30x+25\)
\(b,\left(2x-1\right)^3=8x^3-12x^2+6x-1\)
\(c,\left(3y+2x\right)\left(2x-3y\right)=4x^2-9y^2\)